Autor:Dr.sc. Qamil Haxhibeqiri, Mr.sc. Melinda Mula, Mr.sc. Ramadan LimaniMbshtetur nga Prof. Dr. Joachim Schroeder

Matematika dhemsimdhnia e matematiksudhzues pr klasat 1 - 5

Ministria e Arsimit, Shkencs dhe TeknologjisMinistarstvo Obrazovanja, Nauke i TehnologijeMinistry of Education, Science and Technology

Matematika dhe msimdhnia e matematiks

Udhzues pr klasat 1 - 5

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Autort:Dr.sc. Qamil Haxhibeqiri, Mr.sc. Melinda Mula, Mr.sc. Ramadan Limani, mbeshtetur nga Dr. Joachim Schroeder

Dizajni dhe faqosja nga: Envinion, Prishtin

Prishtin, Prill 2012

Copyright2011. Deutsche Gesellschaft fr Internationale Zusammenarbeit (GIZ) GmbH dhe Qendra pr Arsim e Kosovs (KEC)T gjitha t drejtat i prkasin Deutsche Gesellschaft fr Internationale Zusammenarbeit (GIZ) GmbH projekti Zhvillimi i Kapaciteteve n Sektorin e Arsimit Fillor n Kosov dhe Qendrs pr Arsim t Kosovs (KEC). Ky material, ose pjes t tij, nuk mund t ndrysho-hen n fardo mnyre, pa t drejtat autoriale. Kopje t tij mund t bhen, ose n mnyr elektronike ose mekanike, prmes fotokopjimit apo n mnyra t tjera, por pa ndrhyr n tekstin origjinal.

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PrmbajtjaHyrja ..................................................................................................................................................................................................................................... 6Programi Matematika dhe Msimdhnia e Matematiks pr klasat 1-5 .................................................................................. 8Profili i Kompetencave t Msimdhnsve .................................................................................................................................................... 9I. Bashksit dhe veprimet me to ......................................................................................................................................................................12

1.1. Kuptimi i bashksis. Elementet e bashksis .........................................................................................................121.2. Nnbashksia. Bashksit e barabarta. .........................................................................................................................161.3 Veprimet me bashksi ................................................................................................................................................................191.4. ifti i renditur. Prodhimi i drejtprdrejt (kartezian) i bashksive .............................................................251.5. Parimi i prfshirje - prjashtimit (pr ata q duan t din m shum) .................................................291.6. Relacionet ..........................................................................................................................................................................................32

II. Numrat natyror dhe veprimet me ta ........................................................................................................................................................362.1. Kuptimi i numrit natyror dhe numrorit ........................................................................................................................362.2. Krahasimi i numrave natyror dhe renditja e tyre .................................................................................................372.1. Krahasimi i dy numrave t shkruar (numrorve) ..................................................................................................39

2.1.1. Njri nga numrat ka m shum shifra se tjetri ........................................................................................392.1.2 Dy numrat kan numr t njjt shifrash ......................................................................................................392.1.3. Shkrimi dhe leximi i numrave (numrorve). ..............................................................................................402.1.4. Veprimet me numra natyror .................................................................................................................................43

2.1.4.1. Mbledhja ..................................................................................................................................................................432.1.4.2. Zbritja ........................................................................................................................................................................452.1.4.3. Shumzimi ..............................................................................................................................................................492.1.4.4. Fuqizimi ....................................................................................................................................................................542.1.4.5. Pjestimi ..................................................................................................................................................................55

2.1.4.5.1. Pjestimi pa mbetje .............................................................................................................................552.1.4.5.2. Pjestimi me mbetje ............................................................................................................................562.1.4.5.3 Veti t pjestimit .....................................................................................................................................57

2.1.4.6. Shumfishi m i vogl i prbashkt dhe pjestuesi m i madh i prbashkt ..........612.1.4.7. Shprehjet numerike. Radha e kryerjes s veprimeve .................................................................64

2.1.4.7.1. Vlera e shprehjes numerike. Radha e kryerjes s veprimeve ...................................652.1.4.8. Zbatime. Ekuacionet dhe inekuacionet .................................................................................................66

2.1.4.8.1. Zgjidhja e ekuacioneve t formave x+b=c, xb=c, ax=c ............................................672.1.4.8.2. Zgjidhja e ekuacioneve t formave : ax=b, x:a=b, a:x=b, axb=c, x:ab=c, a:xb=c .......702.1.4.8.3. Zgjidhja e inekuacioneve t formave axbb ..............74

2.1.4.9. Vargjet numerike ................................................................................................................................................78

III. Thyesat .......................................................................................................................................................................................................................813.1. Kuptimi i thyess. .........................................................................................................................................................................813.2. Disa raste t veanta t thyesave ....................................................................................................................................85

3.2.1. Thyesat me numrues 0 ............................................................................................................................................853.2.2. Thyesat me emrues 0 ...............................................................................................................................................863.2.3. Thyesat me emrues 1 ...............................................................................................................................................863.2.4. Thyesat me emrues dhe numrues t barabart ....................................................................................873.2.5. Thyesa t anasjellta (inverse) ...............................................................................................................................87

3.4. Krahasimi i thyesave. Disa lloje t thyesave .............................................................................................................923.4.1 Krahasimi i thyesave me njsin (t plotn) ...............................................................................................923.4.2. Numrat e przier (pr ata q duan t din m shum) ......................................................................933.4.3. Krahasimi i thyesave me emrues t njjt si dhe i thyesave me numrues t njjt ..953.4.4. Krahasimi i thyesave me emrues t ndryshm .......................................................................................96

3.5. Veprimet me thyesa ....................................................................................................................................................................993.5.1 Mbledhja dhe zbritja e thyesave ..........................................................................................................................99

3.5.1.1. Mbledhja dhe zbritja e thyesave me emrues t njjt ...........................................................993.5.1.2. Mbledhja dhe zbritja e thyesave me emrues t ndryshm ...............................................101

3.5.2. Shumzimi dhe pjestimi i thyesave .............................................................................................................103

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IV. Matja dhe masat................................................................................................................................................................................................ 1094.1. Matja e vijave ..............................................................................................................................................................................1104.2. Matja e siprfaqeve .......................................................................................................................................................